Two other would-be GOP contenders — former Alaska Gov. and 2008 vice presidential nominee Sarah Palin and former Massachusetts Gov. Mitt Romney — also appear to have stayed away, though their political action committees did not return multiple requests for comment.

Romney has said Obama, who has visited the region four times since the April 20 explosion of the Deepwater Horizon rig, is “totally out of his depth,” and Palin told him he needed to “get involved, sir.”

Among other potential 2012 candidates, House Republican Conference Chairman Mike Pence (Ind.) plans to visit sometime this summer, his spokeswoman said, while former Arkansas Gov. Mike Huckabee (R) recently moved to Walton County, Fla., near Pensacola, one of the areas of the state most profoundly affected by the spill.

"Gov. Huckabee doesn't have to make a trip there — he lives there and is a resident of Walton County," Huckabee spokesman Hogan Gidley said. "In addition to already seeing for himself, he has talked to his neighbors, friends and people in the area who are in tourism, real estate, shrimping and retail."

Huckabee's presence in the region might earn him some of the political cachet that two other potential candidates, Louisiana Gov. Bobby Jindal (R) and Mississippi Gov. Haley Barbour (R), have gained as their states have been deeply affected by the spill.

Both Jindal and Barbour have received heavy media exposure for their response to the spill. Jindal has been vocal in pushing the Obama administration on its response, having tangled with the administration over a plan to build barrier islands to protect the Louisiana coast from oil coming onshore. Jindal has also pushed the president to end his six-month moratorium on deepwater offshore drilling, as has Barbour, the subject of a prominent profile last weekend in The New York Times.

While Gingrich hasn’t visited the affected area, a spokesman says he has been receiving regular updates from Jindal, Barbour and Alabama Gov. Bob Riley (R).

The GOP pack has been critical, to varying degrees, of Obama's handling of what the administration calls the worst environmental disaster in U.S. history. Most criticism has focused on the swiftness of the administration's response, as well as its decision to impose even a temporary drilling moratorium.

Pawlenty chided Obama for not having taken personal responsibility for the crisis sooner, while Palin went further still.

"Mr. President: with all due respect, you have to get involved, sir. The priorities and timeline of an oil company are not the same as the public’s," she wrote in a Facebook note. "You cannot outsource the cleanup and the responsibility and the trust to BP and expect that the legitimate interests of Americans adversely affected by this spill will somehow be met."

Of the president's four visits to the affected region, the most recent came during a two-day trip last week to Mississippi, Alabama and Florida.